Refers to Dawson from the WB series Dawsons Creek. People with this complex over-analyze everything, and in turn are not able to enjoy anything. They are melodramatic, broody and imploring.

"You're not gonna go all Dawson on me everytime I have a boyfriend, are you?"
From "Buffy the vampire slayer".
(Buffy to Angel, referring to her relationship with Spike, another vampire.)
Dawson complex